Applied

Sta#s#cs and Econometrics II Class Discussion - Simultaneous Equa#ons Models

Es#ma#ng Supply and Demand in the World Oil Market

Structural model

techniques and provide a useful benchmark for assessing relaxed in future work.11 The structural form of this model is given by: demand: qd pt ; xt = bd pt + x9 bd + ed t x t p t supply: qs pt ; xt = bs pt + x9 bs + es t p t x t market clearing: qd pt ; xt = qs pt ; xt = qt t t where xt is a vector f variables characterizing the market for oil which simplifies oto:

If we try to es#mate the equa#ons of this model sed demand: qt = bd pt + x9 bd + eparately by OLS, we have two p t x t basic problems: 1) Iden#ca#on Since the equilibrium price and quan#ty are endogenous, OLS supply: qt = bs pt + x9 bs + es : p t x t es#mates will not be consistent. Therefore, we need instruments. 2) Lack of eciency If there exist restric#ons in the parameters of the equa#ons, a joint es#ma#on will provide more eciency rela#ve to equa#on-by-equa#on OLS.

cation problem and an efficiency p problem, instrumental variables te Es#ma#on methodology restrictions on both the supply and d Assume that the vector xt can be decomposed into four can that the vector of covariates xt
components:

d xt = xt ;

s n xt ; xt ;

c xt ; t

xtd, xts : sets of exogenous demand and supply shiTers where the demand shifters xd are

exo xtn : set of endogenous variables which may enter the but not qua#on the supply curve; where the s supply or demand e shift the supply curve but not the xtc : set of exogenous variables which aect both supply de
and demand.

Substituting xt = xt ; xt ; xt ; xt , into the structural equations (2) and demand and supply, respectively, one gets:

Es#ma#on methodology

demand: qt = bd pt + xd 9 bx;dd + xst 9 bx;sd + xn 9 bx;nd + xc 9 bx;cd + ed p t t t t supply:

assump#on of exogenous demand and supply Assumption 1(Exclusion): Inave a vector of instruments (6) and shiTers.] Now we h the expanded structural equations zand supply,, xct). 0 and b s = 0. =(xtd, xts b d = demand t x;s x;d Under Assumption 1, the structural model can be rewritten as: 2)Also, assume that the instruments are correlated with price pt.

Formally, the exclusion d = 0 and x,ss = 0. [previous 1) Assume that x,s restriction is the following.

demand: q = bd p + xd9 b

+ xn 9 b

+ xc 9 b d + ed

Es#ma#on methodology
Cross-equa*on parameter restric*ons Endogenous dependent variables

OLS

Inecient

Lack of iden#ca#on will make the es#mates inconsistent.

SUR

More ecient than OLS Lack of iden#ca#on because of joint will make the es#mates es#ma#on inconsistent. Consistent, but not ecient because of lack of joint es#ma#on Consistent and ecient Consistent and ecient Consistent and ecient

2SLS

3SLS

Data
Monthly data set, 1981-2000 Two measures of price: real average OPEC crude oil price and real average non-OPEC crude oil price Three measures of quan#ty: world oil produc#on, OPEC oil produc#on, and non-OPEC oil produc#on. Demand shiTers: world popula#on, world commercial energy use, world electricity produc#on, world electricity produc#on from oil, world electricity produc#on from gas Supply shiTers: total world rig count and world oil reserves Exogenous market controls: dummy variable for summer months (Jun., Jul., and Aug.) and winter months (Dec., Jan., and Feb.)

Results

ESTIMATING WORLD OIL SUPPLY/DEMAND Table 9

25
a

Demand equa#on

THREE-STAGE LEAST SQUARES (3SLS) ESTIMATES OF MONTHLY DEMAND, IN LOGS Dependent Variable: Log Quantity of Oil Production (million barrels per day) for (1) World (2) OPEC
c

(3) World

(4) Non-OPEC

Log OPEC oil price (1982-1984$/ -0.01 0.44 barrel) (0.02) (0.15) d Log non-OPEC oil price 0.00 -0.19 (1982-1984$/barrel) (0.02) (0.05) 27 ESTIMATING WORLD OIL SUPPLY/DEMAND Monthly Covariates b Summer equa#on -0.01 10 0.01 -0.01 -0.014 Supply dummy (June, July, Table a August) (0.00) (0.02) (0.00) THREE-STAGE LEAST SQUARES (3SLS) ESTIMATES OF MONTHLY SUPPLY,(0.006) IN LOGS Winter dummy (December, 0.00 -0.01 0.00 0.01 January, February) (0.00) (0.02) (0.00) (0.01) Dependent variable is log quantity of oil production (million barrels per day) for -0.017 d Log OPEC oil price (1982-1984$/barrel) (0.002) -0.06 Population, world (billions) 0.32 (0.01) Log non-OPEC oil price (0.17 ) b (1982-1984$/barrel) world Commercial energy use, 0.16 (million kilotons of oil equivalent) (0.07) Monthly Covariates Electricity production, world -0.05 b Annual Covariates GDP, world (trillion 1982-1984$)
(1) World
d

(2) OPEC

(3) World

(4) Non-OPEC

-0.04 (0.02) d -0.12 c 3.16 (0.04) (1.09) d 1.63 (0.39) c -1.13 d

-0.016 (0.002) b 0.34 d -0.05 (0.17) b (0.01) 0.16 (0.07) -0.06

-0.00 (0.01) c -1.01 -0.01 (0.36) d (0.01) -0.47 (0.12) d 0.42 d

Conclusions
The es#mated supply and demand curves were consistent with economic theory in the cases of world demand, non- OPEC demand, however this was not the case for OPEC demand or for most specica#ons for supply. This may suggest that the assump#on of a sta#c and perfectly compe##ve world oil market is perhaps not reasonable for several reasons: 1) Oil produc#on is a capital-intensive process involving large sunk costs.
2) Oil is a nonrenewable resource, with extrac#on costs likely to increase over #me. 3) According to previous literature, among the OPEC countries a par#al market-sharing cartel model seems more adequate than a compe##ve model.